If Opal gives Zane $29, the amount of money she has will be 25% of his. If Zane gives Opal $40, he will have the same amount of money as her. How much money did each of them have?
(a) Zane
(b) Opal
|
Case 1 |
Case 2 |
|
Zane |
Opal |
Zane |
Opal |
Before |
4 u - 29 |
1 u + 29 |
2.5 u + 40 |
2.5 u - 40 |
Change |
+ 29 |
- 29 |
- 40 |
+ 40 |
After |
4 u |
1 u |
2.5 u |
2.5 u |
(a)
25% =
25100 =
14 In Case 1, when Opal gives to Zane, there is an internal transfer of money from Opal to Zane. The total amount that both have remains the same.
In Case 2, when Zane gives to Opal, there is an internal transfer of money from Zane to Opal. The total amount that both have remains the same.
The total amount that both have in Case 1 and Case 2 are the same.
Total amount that Opal and Zane have
= 4 u + 1 u
= 5 u
Amount that Opal and Zane each has in the end for Case 2
= 5 u ÷ 2
= 2.5 u
Amount that Zane has at first is the same in Case 1 and Case 2.
4 u - 29 = 2.5 u + 40
4 u - 2.5 u = 40 + 29
1.5 u = 69
1 u = 69 ÷ 1.5 = 46
Amount that Zane has
= 4 u - 29
= 4 x 46 - 29
= 184 - 29
= $155
(b)
Amount that Opal has
= 1 u + 29
= 1 x 46 + 29
= 46 + 29
= $75
Answer(s): (a) $155; (b) $75